Energy decomposition analysis in free-surface flows: road-map for the direct computation of wave breaking dissipation

A viscous free-surface flow energy decomposition analysis is conducted in the present paper. In the presence of a free surface, the viscous dissipation for a Newtonian liquid can be decomposed into two terms: an enstrophy component and a free-surface deformation component. Equations for such terms in the weakly compressible SPH (WCSPH) formalism are devised. They require the discretization of a volume and a surface integral, respectively. Applying energy conservation, a double-checking of the free surface term is developed and applied, confirming the quality of the surface integral SPH evaluation, even in the presence of moderately fragmented free surface. Application to a large amplitude standing wave with breaking is presented.